1. Preheat the oven to 375°F (190°C).
2. Separate the leaves from the fresh herb stems until you have about a tablespoon of them. Set them aside along with a few whole sprigs of the herbs.
3. Cut the carrots, turnips, parsnips, potatoes, squash, and celery (or celery root) into approximately 1-inch pieces. Cutting the vegetables uniformly promotes even cooking.
4. Transfer the chopped vegetables, shallots, and garlic to a large baking sheet. Drizzle with olive oil, season with kosher salt and black pepper, and sprinkle with the herb leaves. Toss to combine. Place the whole herb sprigs on the sheet with the vegetables.
5. Roast for approximately 45 minutes, or until the vegetables are lightly browned and tender but not overly soft.
6. Remove the whole herb sprigs from the sheet and allow the vegetables to cool for 5 to 10 minutes before serving.